I can see Splatoon picking up a competitive scene, but I can't imagine it being a very large one. Right now, the game is still young and strategies are still being developed, but I can see where the game might hit that "stomp or be stomped" stage where the good players will know the tricks and the bad players will just get trounced, frustrated, then eventually quit. I can't tell if its that there just aren't that many players online or if the game has zero consideration towards grouping like levels to like levels in a match as opposed to dropping level 1's in with a group of 15's+ (when it comes to facing off against guys with 3+ effects per equipment, IT MATTERS) but currently a match can be mostly even, or completely one sided because the stars aligned and the pros got stuck on one side while the newbs got stuck on another.
In the long run, I can't see the game remaining hugely popular simply because there's going to be a player-erected barrier called the skill gap. If pre-mades are paired up against pub groups come August, this situation will only get worse. Chuck in some WTF moments from lag, and I can see people quitting a game they used to enjoy in disgust, simply because they're now spending more time waiting to respawn while the enemy paints the entire map their color.
As proof of this, I point to Planetside 2's air game, which has such a high skill floor most players that want to fly can't cut it. So the air game is generally emptyish, save for those "ace" pilots that shot down all those rookies to the point they're no longer interested in even trying. I expect the same concept to eventually apply to Splatoon. In CoD it's race around, see someone, left trigger, right trigger, target killed. In Splatoon, interaction with other players is a bit more involved than that, and that's where a lot of players will fall behind.
It's a fun game, the depth is there, but I fear Nintendo might need to recognize that the game's roster picker needs to weigh player stats in team make ups (or maybe it already does, it's just horrible at it.) And of course, prioritize throwing pre-mades against pre-mades come August. The game is only fun when the common player's average battle comes out to a maybe 10% difference in map coverage. Not surprisingly, while the pre-mades and skilled players might enjoy mass farming their victims, their victims do not like being farmed.